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If l1, m1, n1 and l2, m2, n2 are the dir...

If `l_1, m_1, n_1` and `l_2, m_2, n_2` are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are `m_1n_2-m_2n_2, n_1l_2-n_2l_1, l_1m_2-l_2m_1`

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A N EXCEL PUBLICATION-THREE DIMENSTIONAL GEOMETRY-QUESTION BANK
  1. In the following cases, find the distance of each of the given point f...

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  2. Show that the line joining the origin to the point (2, 1, 1) is perpen...

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  3. If l1, m1, n1 and l2, m2, n2 are the direction cosines of two mutually...

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  4. Find the angle between the lines whose direction ratios are a, b, c an...

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  5. Find the equation of a line parallel to x-axis and passing through the...

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  6. If the co-ordinates of the points A, B, C, D be (1,2,3),(4,5,7) (-4,3,...

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  7. If the lines (x-1)/-3 = (y-2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 ...

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  8. Find the vector equation of the line passing through (1,2,3) and perp...

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  9. Find the eqation of the plane passing through (a,b,c) and parallel to ...

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  10. Find the shortest distance between the lines vecr = 6hati+2hatj+2hatk+...

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  11. Find the co-ordinates of the point where the line through (5,1,6) and ...

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  12. Find the co-ordinates of the point where the line through (5,1,6) and ...

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  13. Find the co-ordinates of the point where the line through (3, -4, -5) ...

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  14. Find the equation of the Plane passing through one point (-1,3,2) and ...

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  15. If the points (1,1,p) and (-3,0,1) be equidistant from the plane vecr....

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  16. Find the equation of the plane passing through the line of intersectio...

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  17. If O be the origin and the co-ordinates of P be (1,2,-3), then find th...

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  18. Find the equation of the plane which contains the line of intersectio...

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  19. Find the distance of the point (-1,-5,-10) from the point of intersecț...

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  20. Find the vector equation of the line passing through (1,2,3) and paral...

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